file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/CategoryTheory/Preadditive/Schur.lean | CategoryTheory.finrank_endomorphism_eq_one | [
{
"state_after": "C : Type u_2\ninst✝⁴ : Category C\ninst✝³ : Preadditive C\n𝕜 : Type u_3\ninst✝² : Field 𝕜\ninst✝¹ : IsAlgClosed 𝕜\ninst✝ : Linear 𝕜 C\nX : C\nisIso_iff_nonzero : ∀ (f : X ⟶ X), IsIso f ↔ f ≠ 0\nI : FiniteDimensional 𝕜 (X ⟶ X)\nid_nonzero : 𝟙 X ≠ 0\n⊢ finrank 𝕜 (X ⟶ X) = 1",
"state_b... | [
133,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.toRelIsoLT_apply | [] | [
1021,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_iSup_map_of_injective | [] | [
426,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.tan_eq_sin_div_cos | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(tan x) = ↑(sin x / cos x)",
"tactic": "simp [tan_eq_sin_div_cos]"
}
] | [
1226,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
8
] |
Mathlib/Algebra/CharP/Basic.lean | multiset_sum_pow_char | [] | [
418,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Topology/MetricSpace/PartitionOfUnity.lean | Metric.exists_continuous_nNReal_forall_closedBall_subset | [
{
"state_after": "case intro.intro\nι : Type u_2\nX : Type u_1\ninst✝ : MetricSpace X\nK U : ι → Set X\nhK : ∀ (i : ι), IsClosed (K i)\nhU : ∀ (i : ι), IsOpen (U i)\nhKU : ∀ (i : ι), K i ⊆ U i\nhfin : LocallyFinite K\nδ : C(X, ℝ≥0)\nhδ0 : ∀ (x : X), 0 < ↑δ x\nhδ : ∀ (i : ι) (x : X), x ∈ K i → EMetric.closedBall... | [
138,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Topology/Bases.lean | Set.PairwiseDisjoint.countable_of_isOpen | [
{
"state_after": "case intro.intro.intro\nα : Type u\nt : TopologicalSpace α\ninst✝ : SeparableSpace α\nι : Type u_1\ns : ι → Set α\na : Set ι\nh : PairwiseDisjoint a s\nha : ∀ (i : ι), i ∈ a → IsOpen (s i)\nh'a : ∀ (i : ι), i ∈ a → Set.Nonempty (s i)\nu : Set α\nu_dense : Dense u\nu_encodable : Encodable ↑u\n⊢... | [
366,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.sub | [
{
"state_after": "α : Type u_2\nβ : Type ?u.632866\nm : MeasurableSpace α\nL : Type ?u.632872\nM✝ : Type ?u.632875\nN : Type u_3\ninst✝⁸ : AddCommMonoid L\ninst✝⁷ : TopologicalSpace L\ninst✝⁶ : AddCommMonoid M✝\ninst✝⁵ : TopologicalSpace M✝\ninst✝⁴ : AddCommMonoid N\ninst✝³ : TopologicalSpace N\nv : VectorMeasu... | [
1137,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.sup_mono | [] | [
71,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_comm | [] | [
192,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.coe_lt_inducedMap_iff | [
{
"state_after": "case refine_1\nF : Type ?u.20995\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.21004\ninst✝³ : LinearOrderedField α\ninst✝² : ConditionallyCompleteLinearOrderedField β\ninst✝¹ : ConditionallyCompleteLinearOrderedField γ\ninst✝ : Archimedean α\na : α\nb : β\nq : ℚ\nh : ↑q < inducedMap α β a\n⊢ ↑q < ... | [
224,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Data/List/Basic.lean | List.insertNth_succ_nil | [] | [
1601,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1600,
1
] |
Mathlib/Topology/Constructions.lean | isClosedMap_toMul | [] | [
121,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_zero | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.9461654\n𝕜 : Type ?u.9461657\nE : Type u_1\nF : Type ?u.9461663\nA : Type ?u.9461666\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\n⊢ (∫ (x : ℝ) in a..b, 0 ∂μ) = ... | [
464,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.list_findIdx₁ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.156112\nδ : Type ?u.156115\nσ : Type ?u.156118\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\np : α → β → Bool\nhp : Primrec₂ p\na : β\nl : List β\nn... | [
777,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Data/Set/Prod.lean | Set.preimage_swap_prod | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.30243\nδ : Type ?u.30246\ns✝ s₁ s₂ : Set α\nt✝ t₁ t₂ : Set β\na : α\nb : β\ns : Set α\nt : Set β\nx : β\ny : α\n⊢ (x, y) ∈ Prod.swap ⁻¹' s ×ˢ t ↔ (x, y) ∈ t ×ˢ s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.30243\nδ : Type ?u... | [
269,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.conGen_idem | [] | [
558,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_mul_of_pos_left | [] | [
164,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.close_close | [] | [
148,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_insertSorted | [
{
"state_after": "no goals",
"state_before": "ctx : Context\nk : Nat\nv : Var\np : Poly\n⊢ denote ctx (insertSorted k v p) = denote ctx p + k * Var.denote ctx v",
"tactic": "match p with\n| [] => simp\n| (k', v') :: p => by_cases h : Nat.blt v v' <;> simp [h, denote_insertSorted]"
},
{
"state_af... | [
281,
81
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
278,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.one_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝⁴ : CommSemiring R\nA : Type v₁\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nB : Type v₂\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nx : A ⊗[R] B\n⊢ ↑(↑mul (1 ⊗ₜ[R] 1)) x = x",
"tactic": "refine TensorProduct.induction_on x ?_ ?_ ?_ <;> simp (... | [
425,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Data/Set/Sups.lean | Set.image_sup_prod | [
{
"state_after": "α : Type u_1\ninst✝ : SemilatticeSup α\ns✝ s₁ s₂ t✝ t₁ t₂ u v : Set α\na b c : α\ns t : Set α\nthis : (uncurry fun x x_1 => x ⊔ x_1) '' s ×ˢ t = image2 (fun x x_1 => x ⊔ x_1) s t\n⊢ (uncurry fun x x_1 => x ⊔ x_1) '' s ×ˢ t = s ⊻ t",
"state_before": "α : Type u_1\ninst✝ : SemilatticeSup α\n... | [
191,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_le_iff_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.90112\nα : Type u_1\nβ : Type ?u.90118\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a \\ b ≤ b ↔ a ≤ b",
"tactic": "rw [sdiff_le_iff, sup_idem]"
}
] | [
525,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_iUnion | [] | [
141,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.WF.out | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ncmp : α → α → Ordering\nt : RBNode α\nh : WF cmp t\n⊢ Ordered cmp t ∧ ∃ c n, Balanced t c n",
"tactic": "induction h with\n| mk o h => exact ⟨o, _, _, h⟩\n| insert _ ih => have ⟨o, _, _, h⟩ := ih; exact ⟨o.insert, h.insert⟩\n| erase _ ih => hav... | [
470,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
466,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.symm | [
{
"state_after": "no goals",
"state_before": "x y z : ℤ\nh : PythagoreanTriple x y z\n⊢ PythagoreanTriple y x z",
"tactic": "rwa [pythagoreanTriple_comm]"
}
] | [
74,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.NonemptyCompacts.isCompact | [] | [
229,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
11
] |
Mathlib/Data/List/Basic.lean | List.head!_eq_head? | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.41398\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : Inhabited α\nl : List α\n⊢ head! l = Option.iget (head? l)",
"tactic": "cases l <;> rfl"
}
] | [
860,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace/HasColimits.lean | AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality | [
{
"state_after": "J : Type u'\ninst✝⁴ : Category J\nC : Type u\ninst✝³ : Category C\ninst✝² : HasColimitsOfShape J TopCat\ninst✝¹ : ∀ (X : TopCat), HasLimitsOfShape Jᵒᵖ (Presheaf C X)\ninst✝ : HasLimitsOfShape Jᵒᵖ C\nF : J ⥤ PresheafedSpace C\ns : Cocone F\nU V : (Opens ↑↑s.pt)ᵒᵖ\ni : U ⟶ V\n⊢ s.pt.presheaf.map... | [
292,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | Monotone.Iio | [] | [
89,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
11
] |
Mathlib/Data/List/Sublists.lean | List.sublists'_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nl : List α\n⊢ sublists' (a :: l) = sublists' l ++ map (cons a) (sublists' l)",
"tactic": "simp [sublists'_eq_sublists'Aux, foldr_cons, sublists'Aux_eq_map]"
}
] | [
81,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.comp_toLinearMap_symm_eq | [
{
"state_after": "case mp.h\nR : Type ?u.199169\nR₁ : Type u_5\nR₂ : Type u_1\nR₃ : Type u_2\nk : Type ?u.199181\nS : Type ?u.199184\nM : Type ?u.199187\nM₁ : Type u_6\nM₂ : Type u_3\nM₃ : Type u_4\nN₁ : Type ?u.199199\nN₂ : Type ?u.199202\nN₃ : Type ?u.199205\nN₄ : Type ?u.199208\nι : Type ?u.199211\nM₄ : Type... | [
443,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Init/IteSimp.lean | if_false_right_eq_and | [
{
"state_after": "no goals",
"state_before": "p : Prop\nh : Decidable p\nq : Prop\n⊢ (if p then q else False) = (p ∧ q)",
"tactic": "by_cases p <;> simp [h]"
}
] | [
35,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.stalkToFiberRingHom_toStalk | [] | [
569,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Data/Pi/Lex.lean | Pi.isTrichotomous_lex | [
{
"state_after": "case inl\nι : Type u_2\nβ : ι → Type u_1\nr : ι → ι → Prop\ns : {i : ι} → β i → β i → Prop\ninst✝ : ∀ (i : ι), IsTrichotomous (β i) s\nwf : WellFounded r\na b : (i : ι) → β i\nhab : a = b\n⊢ Pi.Lex r s a b ∨ a = b ∨ Pi.Lex r s b a\n\ncase inr\nι : Type u_2\nβ : ι → Type u_1\nr : ι → ι → Prop\n... | [
93,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Filter.Tendsto.isCoboundedUnder_ge | [] | [
64,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_subtype_eq_finprod_cond | [] | [
1007,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1005,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.prod_mk_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf : α → β\nx y : α\nr : ℝ≥0∞\na : α\n⊢ LipschitzWith 1 (Prod.mk a)",
"tactic": "simpa only [max_eq_right zero... | [
255,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
11
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | isBounded_ge_nhds | [] | [
89,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.integrable_approxOn_range | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.1025603\nβ : Type ?u.1025606\nι : Type ?u.1025609\nE : Type ?u.1025612\nF : Type ?u.1025615\n𝕜 : Type ?u.1025618\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : BorelSpace E\nf : β → E\nμ : Measure β\... | [
270,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.map_dvd | [] | [
659,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
11
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | EMetric.preimage_mul_right_ball | [
{
"state_after": "M : Type u\nG : Type v\nX : Type w\ninst✝⁵ : PseudoEMetricSpace X\ninst✝⁴ : Group G\ninst✝³ : MulAction G X\ninst✝² : IsometricSMul G X\ninst✝¹ : PseudoEMetricSpace G\ninst✝ : IsometricSMul Gᵐᵒᵖ G\na b : G\nr : ℝ≥0∞\n⊢ (fun x => x * a) ⁻¹' ball b r = ball (b * a⁻¹) r",
"state_before": "M :... | [
313,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.358141\nγ : Type ?u.358144\nι : Type ?u.358147\nM : Type u_2\nM' : Type ?u.358153\nN : Type ?u.358156\nP : Type ?u.358159\nG : Type ?u.358162\nH : Type ?u.358165\nR : Type ?u.358168\nS : Type ?u.358171\ninst✝ : Zero M\np : α → Prop\nf :... | [
905,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.one_mem_centralizer | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nS T : Set M\ninst✝ : MulOneClass M\n⊢ 1 ∈ centralizer S",
"tactic": "simp [mem_centralizer_iff]"
}
] | [
62,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/SpecialFunctions/Bernstein.lean | bernstein.probability | [
{
"state_after": "n : ℕ\nx : ↑I\nthis : ∑ ν in Finset.range (n + 1), bernsteinPolynomial ℝ n ν = 1\n⊢ ∑ k : Fin (n + 1), ↑(bernstein n ↑k) x = 1",
"state_before": "n : ℕ\nx : ↑I\n⊢ ∑ k : Fin (n + 1), ↑(bernstein n ↑k) x = 1",
"tactic": "have := bernsteinPolynomial.sum ℝ n"
},
{
"state_after": "n... | [
115,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\nH : ¬1 = 0\n⊢ support X = {1}",
"tactic": "rw [← pow_one X, support_X_pow H 1]"
}
] | [
912,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.mono_measure | [] | [
518,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.symm_apply_eq | [] | [
407,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | continuousWithinAt_inv | [] | [
211,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.forall_fin_one | [] | [
1760,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1759,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.toFun_eq_coe | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.zero_mem_smul_finset_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.935966\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.935975\ninst✝⁴ : Zero α\ninst✝³ : Zero β\ninst✝² : SMulWithZero α β\ninst✝¹ : DecidableEq β\ns : Finset α\nt : Finset β\ninst✝ : NoZeroSMulDivisors α β\na : α\nha : a ≠ 0\n⊢ 0 ∈ a • t ↔ 0 ∈ t",
"tac... | [
2133,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2132,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithZero.coe_div | [] | [
314,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Order/Heyting/Basic.lean | snd_sdiff | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullback_map_embedding_of_embeddings | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z✝ W X Y Z S T : TopCat\nf₁ : W ⟶ S\nf₂ : X ⟶ S\ng₁ : Y ⟶ T\ng₂ : Z ⟶ T\ni₁ : W ⟶ Y\ni₂ : X ⟶ Z\nH₁ : Embedding ((forget TopCat).map i₁)\nH₂ : Embedding ((forget TopCat).map i₂)\ni₃ : S ⟶ T\neq₁ : f₁ ≫ i₃ = i₁ ≫ g₁\neq₂ : f₂ ≫ i₃ = i₂ ≫ g₂\n⊢ Embeddin... | [
264,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Computability/Reduce.lean | transitive_manyOneReducible | [] | [
73,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.int_mul_sub_eq | [] | [
258,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Computability/Halting.lean | ComputablePred.computable_iff_re_compl_re' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nσ : Type ?u.313648\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\np : α → Prop\n⊢ ComputablePred p ↔ RePred p ∧ RePred fun a => ¬p a",
"tactic": "classical exact computable_iff_re_compl_re"
},
{
"state_after": "no goals",
"state_be... | [
265,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signAux3_mul_and_swap | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\ns : Multiset α\nhs : ∀ (x : α), x ∈ s\nl : List α\nhl : Quotient.mk (List.isSetoid α) l = s\n⊢ signAux3 (f * g) hs = signAux3 f hs * signAux3 g hs ∧ ∀ (x y : α), x ≠ y → signAux3 (swap x y) hs = -1",
"state_be... | [
534,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Analysis/Normed/Ring/Seminorm.lean | RingNorm.ext | [] | [
209,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.mem_edgeSet | [] | [
243,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_eq_zero' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.1228006\n𝕜 : Type ?u.1228009\nα : Type ?u.1228012\nι : Type ?u.1228015\nκ : Type ?u.1228018\nE : Type u_1\nF : Type ?u.1228024\nG : Type ?u.1228027\ninst✝¹ : NormedGroup E\ninst✝ : NormedGroup F\na b : E\n⊢ ‖a‖₊ = 0 ↔ a = 1",
"tactic": "rw [← N... | [
2013,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2012,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.one_symm | [] | [
147,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.memℒp_two_iff_integrable_sq_norm | [
{
"state_after": "α : Type u_1\nF : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup F\nf : α → F\nhf : AEStronglyMeasurable f μ\n⊢ Memℒp f 2 ↔ Memℒp (fun x => ‖f x‖ ^ 2) 1",
"state_before": "α : Type u_1\nF : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGro... | [
56,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Init/Logic.lean | decide_False' | [
{
"state_after": "no goals",
"state_before": "a b c d : Prop\np : ?m.25417\nh : Decidable False\n⊢ decide False = false",
"tactic": "simp"
}
] | [
276,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/List/Zip.lean | List.unzip_nil | [] | [
204,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.coe_measureUnivNNReal | [] | [
3088,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3086,
1
] |
Mathlib/Data/Finset/Sigma.lean | Finset.sigmaLift_eq_empty | [
{
"state_after": "ι : Type u_1\nα : ι → Type u_3\nβ : ι → Type u_4\nγ : ι → Type u_2\ninst✝ : DecidableEq ι\nf g : ⦃i : ι⦄ → α i → β i → Finset (γ i)\na : (i : ι) × α i\nb : (i : ι) × β i\n⊢ (if h : a.fst = b.fst then map (Embedding.sigmaMk b.fst) (f (h ▸ a.snd) b.snd) else ∅) = ∅ ↔\n ∀ (h : a.fst = b.fst), ... | [
179,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsOrthoᵢ.separatingRight_iff_not_isOrtho_basis_self | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.611950\nR₂ : Type ?u.611953\nR₃ : Type ?u.611956\nM : Type u_2\nM₁ : Type ?u.611962\nM₂ : Type ?u.611965\nMₗ₁ : Type ?u.611968\nMₗ₁' : Type ?u.611971\nMₗ₂ : Type ?u.611974\nMₗ₂' : Type ?u.611977\nK : Type ?u.611980\nK₁ : Type ?u.611983\nK₂ : Type ?u.611986\nV : Type ... | [
827,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | limit_zero_of_norm_tendsto_zero | [] | [
90,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Topology/SubsetProperties.lean | Nat.cocompact_eq | [] | [
551,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
9
] |
Mathlib/Data/Set/Function.lean | Function.RightInverse.rightInvOn | [] | [
1608,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1607,
1
] |
Mathlib/Data/Multiset/Sum.lean | Multiset.disjSum_mono_left | [] | [
80,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/RingTheory/Valuation/Integers.lean | Valuation.Integers.one_of_isUnit | [
{
"state_after": "R : Type u\nΓ₀ : Type v\ninst✝⁵ : CommRing R\ninst✝⁴ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nO : Type w\ninst✝³ : CommRing O\ninst✝² : Algebra O R\ninst✝¹ : CommRing O\ninst✝ : Algebra O R\nhv : Integers v O\nx : O\nhx : IsUnit x\nu : Oˣ\nhu : ↑u = x\n⊢ ↑v (↑(algebraMap O R) x... | [
80,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.not_mem_of_dist_lt_infDist | [] | [
534,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.ndrec_mk | [] | [
345,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.if' | [] | [
3101,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3098,
11
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value_Ioo | [] | [
151,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.inf_apply | [] | [
433,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_le | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.999867\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\ninst✝ : SeminormedAddCommGroup β\nf g : α →ᵇ β\nx : α\nC : ℝ\nC0 : 0 ≤ C\n⊢ ‖f‖ ≤ C ↔ ∀ (x : α), ‖↑f x‖ ≤ C",
"tactic": "simpa using @dist_le _ _ _ _ f 0 _ C0"
}
] | [
842,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Topology/Order/Basic.lean | induced_orderTopology | [] | [
1054,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.edgeDensity_nonneg | [] | [
403,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualRestrict_apply | [] | [
793,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.fg_of_linearEquiv | [] | [
238,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientMap_algebraMap | [] | [
351,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Algebra/Module/Basic.lean | nsmul_eq_smul_cast | [
{
"state_after": "case zero\nα : Type ?u.130390\nR : Type u_2\nk : Type ?u.130396\nS : Type ?u.130399\nM : Type u_1\nM₂ : Type ?u.130405\nM₃ : Type ?u.130408\nι : Type ?u.130411\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : M\n⊢ Nat.zero • b = ↑Nat.zero • b\n\ncase succ\nα : Type ?u.13... | [
395,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | maximal_orthonormal_iff_basis_of_finiteDimensional | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1127153\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\nv : Set E\ninst✝ : FiniteDimensional 𝕜 E\nhv : Orthonormal 𝕜 Subtype.val\nt... | [
1346,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1335,
1
] |
Mathlib/Data/Matrix/Basic.lean | RingEquiv.mapMatrix_symm | [] | [
1571,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1570,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_pow_eq_sum | [] | [
606,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Logic/Equiv/Option.lean | Equiv.optionSubtype_symm_apply_symm_apply | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.28780\ninst✝ : DecidableEq β\nx : β\ne : α ≃ { y // y ≠ x }\nb : { y // y ≠ x }\n⊢ ↑b = x → False",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.28780\ninst✝ : DecidableEq β\nx : β\ne : α ≃ { y // y ≠ x }\nb : { y // y ≠ x }\n⊢ ↑(↑(↑(opti... | [
268,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_zero_mul_coeff | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nr : R\nx : HahnSeries Γ R\na : Γ\n⊢ coeff (↑(single 0) r * x) a = r * coeff x a",
"tactic": "rw [← add_zero a, single_mul_coeff_add, add_zero]"
}
] | [
753,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_one_iff_of_pos | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 0 < x\n⊢ x ^ y < 1 ↔ 1 < x ∧ y < 0 ∨ x < 1 ∧ 0 < y",
"tactic": "rw [rpow_def_of_pos hx, exp_lt_one_iff, mul_neg_iff, log_pos_iff hx, log_neg_iff hx]"
}
] | [
557,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullbackIsoProdSubtype_hom_snd | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nX Y Z : TopCat\nf : X ⟶ Z\ng : Y ⟶ Z\n⊢ (pullbackIsoProdSubtype f g).hom ≫ pullbackSnd f g = pullback.snd",
"tactic": "rw [← Iso.eq_inv_comp, pullbackIsoProdSubtype_inv_snd]"
}
] | [
133,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Algebra/Parity.lean | even_abs | [
{
"state_after": "case inl\nF : Type ?u.48526\nα : Type u_1\nβ : Type ?u.48532\nR : Type ?u.48535\ninst✝¹ : SubtractionMonoid α\ninst✝ : LinearOrder α\na : α\nh✝ : abs a = a\n⊢ Even (abs a) ↔ Even a\n\ncase inr\nF : Type ?u.48526\nα : Type u_1\nβ : Type ?u.48532\nR : Type ?u.48535\ninst✝¹ : SubtractionMonoid α\... | [
204,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_iInter₂_of_mem | [] | [
176,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.iterate | [] | [
2484,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2481,
11
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.curry0_apply | [] | [
1635,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1633,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cast_pos | [] | [
684,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_lt_toNNRat_iff' | [
{
"state_after": "no goals",
"state_before": "p q : ℚ\n⊢ toNNRat q < toNNRat p ↔ q < p ∧ 0 < p",
"tactic": "simp [← coe_lt_coe, toNNRat, lt_irrefl]"
}
] | [
366,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Data/Set/Basic.lean | Set.eq_of_inclusion_surjective | [
{
"state_after": "α : Type u_1\ns✝ t✝ u s t : Set α\nh : s ⊆ t\nh_surj : Surjective (inclusion h)\nx : α\nhx : x ∈ t\n⊢ x ∈ s",
"state_before": "α : Type u_1\ns✝ t✝ u s t : Set α\nh : s ⊆ t\nh_surj : Surjective (inclusion h)\n⊢ s = t",
"tactic": "refine' Set.Subset.antisymm h (fun x hx => _)"
},
{
... | [
2816,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2812,
1
] |
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